savage vs rem is like ford vrs dodge, they both have ups and downs, personally i own both and have no quams with it.
the 308 as a good caliber and will be able to reach pretty far out...
if i may put in my .02... if your just getting into the precission rifle aspect, maybe loook at a .223, its got a few advantages over a 308 for starting, its cheaper for both buying and reloading, and while the recoild on a 308 isnt bad, it is enough that it can devlope bad habbits. chances are with a 223, once you have every thing learnt - breathing, tirgger controll, proper position etc and have practiced endlessly, the barrel will be shot off, and you can rebarrel with a nice match barrel with a fast twist, and shoot the real heavies and get out to 1000 yards with it.
the 308 is still affordable to shoot but if your dont have the dilligence to practice proper technique, its easy to fall into bad habbits.